Aktuelles & Events

In this talk, the author will present recent results for consensus-based and flocking models, with non-universal interaction, time delays, and possible communication failures. In particular, extending previous results, they allow the amount of interaction between the agents over fixed-length time intervals to decay polynomially. For the first-order Hegselmann-Krause type model, they prove asymptotic convergence to consensus, and for the second-order Cucker-Smale model, the authors establish asymptotic flocking under an additional assumption on the decay of the influence function. These results show that collective behavior can still emerge under progressively weakening communication and without requiring strong connectivity of the interaction graph.

The aim of this conference is to bring together experts in quantum, classical and stochastic dynamics to exchange ideas about common methods and results in this broad field of mathematical physics. It will also be an occasion to celebrate the 80th birthday of Herbert Spohn. The conference will take place at the TUM Institute for Advanced Studies (IAS) on the Garching Research Campus and is organised and supported by the CRC TRR352 Mathematics of Many-Body Quantum Systems and Their Collective Phenomena. Registration is free and now open online: https://sites.google.com/view/largescaledynamics2026/home

TBA ____________________________________ Invited by Prof. Helmut Schwichtenberg

Granger causality is commonly formulated through linear prediction in vector autoregressive models, limiting its ability to detect nonlinear predictive relationships. We propose a reproducing kernel Hilbert space (RKHS)-based test for nonlinear Granger non-causality in the conditional mean for nonlinear autoregressive processes. The key idea is a conditional-centering decomposition of the target regression function into an own-history component and an orthogonal component capturing the additional predictive contribution of the potential source history. Non-causality is characterized by the vanishing of the latter component. The own-history component is estimated by kernel ridge regression, and the residuals are embedded in a second RKHS using a conditionally centered kernel. This yields an RKHS-valued residual moment whose squared norm forms the test statistic. We establish a weighted chi-square null limit and consistency against fixed alternatives for the population-centered statistic. An empirically centered version is shown to retain the null limit and enables spectral calibration of critical values and $p$-values without resampling. Simulation studies demonstrate accurate size control and power against nonlinear alternatives, and real-data applications illustrate the method's usefulness for detecting nonlinear predictive relationships in time series.